Dresden, Germany ? Running low on hope and almost out of time, the Americans were surely beat, about to make their earliest exit from the Women’s World Cup.

And then, with one of the most thrilling goals in U.S. history, they weren’t.

Showing a dramatic burst sure to captivate the folks back home, the Americans packed an entire World Cup’s worth of theatrics into a 15-minute span by beating Brazil 5-3 on penalty kicks after a 2-2 tie Sunday night.

Abby Wambach tied it with a magnificent, leaping header in the 122nd minute, and Hope Solo denied the Brazilians — again — in one of the most riveting games in the history of the World Cup, men’s or women’s.

“There is something special about this group. That energy, that vibe,” Solo said. “Even in overtime, you felt something was going to happen.”

The United States advanced to Wednesday’s semifinals against France, which eliminated England on penalty kicks Saturday.

And while the Americans will have to win twice more to win the final, they are the only one of the favorites left after two-time defending champ Germany was stunned by Japan on Saturday night.